Because she has no standing, Stroud said Quets can also not seek visitation rights because that falls under custody in family law.
"[The] plaintiff lost her right to seek custody of or visitation with the children when she consented to their adoption," wrote Stroud.
The case began in 2005 when Quets got pregnant through in-vitro fertilization and gave birth to the children in Florida.
Instead of keeping the twins, Quets allowed an Apex couple, Kevin and Denise Needham, to adopt them.
She later claimed she was sleep deprived and under duress when she signed the paperwork, and hours later decided she wanted them back. Within days, Quets filed suit in Florida asking for custody of the twins, and a judge granted her the right to visit on weekends while the case was being appealed.
The custody fight got national attention in 2006 when Quets kidnapped the children and fled to Canada during a visitation. Quets was arrested, and a judge cancelled her visitation rights. Quets later pleaded guilty to kidnapping charges and was put on probation.
The twins are now 3-years-old.
Reacting to Tuesday's ruling, Needham attorney Barbara Sandlin said they are "very happy with the court's decision."
She said the ruling should put an end to the case in North Carolina, but it's not clear if Quets will now try to appeal to the North Carolina Supreme Court.
A call to Quets' attorney was not immediately returned.
Quets did win a minor victory Tuesday. The Appeals Court overturned an order that she pay $7,480.50 in court costs to the Needhams.